Holomorphic Spinors and the Dirac Equation

In the first part of this paper, the closed spin Kähler manifolds of positive scalar curvature with smallest possible first eigenvalue of the Dirac operator, are characterized by holomorphic spinors. In the second part, the space of holomorphic spinors on a Kähler–Einstein manifold is described by eigenspinors of the square of the Dirac operator and vanishing theorems for holomorphic spinors are proved.